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Q.

If A and B are orthogonal matrices of order 2 such that ABA1 is a symmetric matrix, where A, B and ABA1I,I. Match List-I with List – II and select the correct answer using the code given below the list

Column–I

Column–II

A)

|B| is equal to

P)

0

B)

tr((ABA1)2017) is equal to

Q)

-1

C)

tr(B2) is equal to

R)

1

D)

Sum of elements of  (adjB2)2 is equal to

S)

2

(Note: |X|, tr(X) and adj (X) denote determinant value, trace and adjoint of matrix X respectively).

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a

A–Q, B–P, C–S, D–R

b

A–Q, B–S, C–P, D–R

c

A–Q, B–P, C–R, D–S

d

A–P, B–Q, C–R, D–S

answer is C.

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Detailed Solution

AAT=ATA=I,BBT=BTB=I        Now,  (ABA1)T(ABA1)=(AT)1BTATABA1       =(AT)1A1=(AAT)=I    (ABA1)T(ABA1)=I

(ABA1)T=ABA1(symmetric)

(ABA1)2=IABA1  is involutory matrix and  (ABA1)2017=ABAI

ABA1I,I

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